Lenses of all types may be found in a broad range of applications. A particular use of lenses is in illumination optics. One main purpose of lenses in illumination optics is to confine or direct light into a beam with a controlled angle, thereby directing the light into an intended area of illumination. One way to fulfill this purpose is to ensure that the beam does not have a wide angle.
U.S. Pat. No. 6,717,735 (hereafter the '735 patent), assigned to the assignee of the instant disclosure, and incorporated herein by reference as if fully set forth herein, discloses lens structures for flux redistribution and for optical low pass filtering. Embodiments of the lens structures discussed in the '735 patent include a lens structure that has a surface that includes a seamless profile, which is devoid of cusps. The surface includes a plurality convex elements and concave elements (e.g., an array of alternating convex elements and concave elements). The convex elements include a positive surface curvature area, and the concave elements include a negative surface curvature area. The lens structure can include a surface for producing a controlled amount of under-corrected spherical aberration and over-corrected spherical aberration in relation to a “prototype” surface. The prototype surface corresponds to an optimized sharp lens surface. The surface that defines the controlled amount of under-corrected spherical aberration and over-corrected spherical aberration is shaped according to an odd order polynomial function that when derived, results in an even order polynomial function that defines the lens surface having the spherical aberration. The under-corrected spherical aberration and the over-corrected spherical aberration do not alter the focal point of the lens, but results in an acceptable light flux redistribution.
U.S. Pat. No. 7,400,456 (hereafter the '456 patent), assigned to the assignee of the instant disclosure, and incorporated herein by reference as if fully set forth herein, builds on the lens structure of the '735 patent by introducing a lens structure defined by a cubic polynomial function. The cubic polynomial function evenly distributes the slope perturbation over the entire lens surface resulting in a symmetrical ring pattern of sag perturbations applied to a previously optimized sharp lens. The perturbations consisted of a sequence of segments of cubic polynomial radial functions merged in a continuous sag and slope at the boundary between segments. Each segment was a quarter or half wavelength of a wavy function. The resultant perturbation slope formed a “folded parabolic” function which had the property that each increment of surface slope departure from the optimized sharp lens has exactly the same amount of aperture area assigned to it, as does any other equal slope increment. A disadvantage of this structure is that the same amount of light is placed at the axial image focal point as is placed at the periphery of the deliberately fuzzy spot. This results in the center of the spot being brighter than the rim.
However, it would be desirable to maintain substantially constant light flux per unit area over the entire fuzzy image spot so that the center of the spot is not substantially brighter than the periphery.